On an indoor circular track of circumference 50 feet, Joneal starts at point $S$, runs in a counterclockwise direction, and then stops when he has run exactly one mile (5280 feet). On which quarter of the circle, $A$, $B$, $C$ or $D$, did Joneal stop?

[asy]
import graph;
draw(Circle((0,0),20));
draw((-25,0)--(25,0));
draw((0,-25)--(0,25));
dot((20,0));
label("$S$",(20,0),SE);
label("$A$",(17,17),E);
label("$B$",(-17,17),W);
label("$C$",(-17,-17),W);
label("$D$",(17,-17),E);
[/asy]
Answer: Since 5250 is divisible by 50, Joneal is back at point $S$ after running 5250 feet.  For the next 12.5 feet, he is on the portion of the track marked $A$. For the next 12.5 feet after that, he is on the portion of the track marked $B$.  At this point he has traveled $5250+12.5+12.5=5275$ feet.  After traveling the final 5 feet, he is on the portion of the track marked $\boxed{C}$.